We take it for granted now, but the fact that you can flip your phone from portrait to landscape mode depends on accelerometers. As everyone knows, though, the damn things often get it wrong, leaving you staring at a screen that refuses to reorient until you give it a good shake. One of the reasons for the screen refusing to orient correctly is that accelerometers have to balance sensitivity to small changes with the speed of response—a slow accelerometer is a sensitive accelerometer.

This compromise, however, is also due to fabrication limitations. A recent paper in Nature Photonics shows that clever fabrication can result in an accelerometer that is both fast and sensitive.

An accelerometer works by sensing the motion of a suspended test mass. If suspended test mass doesn't mean a lot to you, think of a device containing a bit of hardware consisting of a spring attached with a weight at the end of it. Every time the device moves, the acceleration will set the mass in motion: the direction and vigor of the acceleration are reflected in the direction and amplitude of the spring's oscillations.

Three factors come into play in determining the performance of an accelerometer. The size of the test mass—the more massive it is, the smaller its oscillations are for a given acceleration. For maximum sensitivity, you want it as light as possible.

The second factor is called the Q of the oscillator. Q is, put simply, a measure of how long it takes the test mass to return to rest after it has been given a shake. A high Q oscillator will oscillate for longer than a low Q oscillator, which makes things easier to detect.

The final factor is the resonant frequency of oscillation, which is where the accelerometer is most sensitive—if we were to shake the accelerometer at just that frequency, we would get a giant oscillation. This, however, is not terribly useful, because we want to detect a lot of different frequencies.

The way to do this is to set the resonance frequency above the maximum acceleration that you want to measure. The response of the test mass to accelerations below that frequency is fairly even across the board. Unfortunately, the response is also substantially less sensitive. In any case, the resonant frequency defines the range of frequency components in an acceleration that you can measure, which determines the speed of the accelerometer's response.

So, the perfect accelerometer has a very tiny test mass that doesn't have a strong resonant response, and that response should be at high frequencies so that it's also fast. Of course, such an accelerometer would pick up every vibration, including those due to thermal noise inside the case of the device; generally not a desirable feature.

Obviously, a grand compromise plus some innovative thinking is required to break this trifecta of embuggerance. This is exactly what a team of researchers from Cal Tech and the University of Rochester have done. They recognized that if you take a very tiny mass and make it part of a very high Q resonator, then the mass will be very insensitive to excitation due to temperature. But if you could measure the amplitude of the oscillations, you could measure very tiny accelerations. The key, then, is in how you measure things.

Researchers created their mass by etching away the surrounds of a silicon nitride membrane (one of the springiest materials known to man), leaving a block with a mass of just 10pg (10-12g) suspended by the same material. That material choice means that the resonance frequency is just under 30kHz, allowing a researcher to potentially sense accelerations at a rate of something like 15kHz (which is fast). So, we have an extremely sensitive accelerometer—now we just need to give it a high Q.

As it turns out, the springy material (silicon nitride) is a great material for making tiny optical components. The researchers fabricated a tiny zipper-like structure next to the mass. The zipper acts like a pair of mirrors that reflects light back and forth—which means the researchers placed an optical resonator right next to their mechanical resonator. As the test mass moves back and forth, it changes the length of the optical resonator ever so slightly, and that changes the frequency of the light that it will resonate.

The upshot is that if you shine a laser light into the optical resonator, then as the mass passes back and forth near the resonator, it causes the amplitude of the light exiting the other side of the resonator to change. The higher the Q of the optical resonator, the more sensitive it becomes. So, even though the test mass is only making the tiniest of motions, the sensing device picks it up with ease.

The researchers show that their accelerometer is very close to the absolute limit of what is allowed by quantum mechanics (in terms of the trade, it is called shot-noise limited).

I should note that this is unlikely to turn up in your phone anytime soon. The problem lies in the detection system: that laser was a relatively expensive device, and if you want your accelerometer for a few pennies, this isn't going to do it for you. I can see this being used in research labs for monitoring vibrational noise, and in motion capture suites, where accelerometers are combined with clever algorithms to calculate absolute motion from measured accelerations.

That material choice means that the resonance frequency is just under 30kHz, allowing a researcher to potentially sense accelerations at a rate of something like 15kHz.

This statement seems to imply a connection between resonance freq. and the Nyquist freq. My signal processing-foo is pretty weak but I'm unaware of any relationship there. Anyone care to explain?

So what I think this is saying is that this system is capable of keeping up with a system where the first derivative of the acceleration has no frequency component greater than 15kHz? That makes more sense to me that stating acceleration (m/s^2) in terms on Hz (1/s).

the problem lies in the detection system: that laser was a relatively expensive device, and if you want your accelerometer for a few pennies, this isn't going to do it for you.

How good of a laser does this require? I would think it could use a low power diode or even laser on a chip... while they aren't pennies to my knowledge (I haven't been paying any attention to the latter in the past few years so no clue where the tech and costs are at now), I would think they're still substantially cheaper than something higher power. Pulsing shouldn't affect measurement in a system like this if you don't need the very highest frequency in your motion polling?

That material choice means that the resonance frequency is just under 30kHz, allowing a researcher to potentially sense accelerations at a rate of something like 15kHz.

This statement seems to imply a connection between resonance freq. and the Nyquist freq. My signal processing-foo is pretty weak but I'm unaware of any relationship there. Anyone care to explain?

So what I think this is saying is that this system is capable of keeping up with a system where the first derivative of the acceleration has no frequency component greater than 15kHz? That makes more sense to me that stating acceleration (m/s^2) in terms on Hz (1/s).

I think it has more to do with wanting to only use the resonator at frequencies far below its resonance frequency in order to stay within a more linear part of its sensitivity regime. Apparently "something like 15kHz" (IE about 50% or less of the resonant frequency) is linear enough (which kinda makes sense, 15kHz would be the major harmonic of 30kHz, anything below that will be substantially more linear).

That material choice means that the resonance frequency is just under 30kHz, allowing a researcher to potentially sense accelerations at a rate of something like 15kHz.

So what I think this is saying is that this system is capable of keeping up with a system where the first derivative of the acceleration has no frequency component greater than 15kHz? That makes more sense to me that stating acceleration (m/s^2) in terms on Hz (1/s).

Actually, while I believe what you said is right, that sentence is (I think) talking about the sampling rate of the accelerometer, not the rate of the accelerations. In other words, it can update how fast it is accelerating 15 thousand times per second, not that the acceleration is changing 15,000 times per second.

This statement seems to imply a connection between resonance freq. and the Nyquist freq. My signal processing-foo is pretty weak but I'm unaware of any relationship there. Anyone care to explain?

So what I think this is saying is that this system is capable of keeping up with a system where the first derivative of the acceleration has no frequency component greater than 15kHz? That makes more sense to me that stating acceleration (m/s^2) in terms on Hz (1/s).

It's not the actual acceleration value that's being stated in Hz, it's the oscillations.

Remember, the n-th derivative or integral of a sinusoid is another sinusoid with the same period, so if you're seeing acceleration oscillate at 15 kHz, you'd also be seeing 15 kHz oscillations in velocity, position, jerk (derivative of acceleration), or however far out you want to take it.

It's nothing to do with sampling frequency or the actual magnitude, and everything to do with staying in the linear sensitivity range, as Alhazred says.

I should note that this is unlikely to turn up in your phone anytime soon. The problem lies in the detection system: that laser was a relatively expensive device, and if you want your accelerometer for a few pennies, this isn't going to do it for you.

Whats the difference between existing phone accelerometers and this design then? Could some of its features be incorporated without a large price hike? And if they could build a cheaper accelerometer based off this design, would it work better?

I should note that this is unlikely to turn up in your phone anytime soon. The problem lies in the detection system: that laser was a relatively expensive device, and if you want your accelerometer for a few pennies, this isn't going to do it for you.

Whats the difference between existing phone accelerometers and this design then? Could some of its features be incorporated without a large price hike? And if they could build a cheaper accelerometer based off this design, would it work better?

The usual form of sensing involves etching a comb structure on the sides of the test mass inter-digitated with a comb on the substrate, and measuring capacitance changes. I suspect in this design the test mass is simply too small to give a good capacitor. Since the capacitor designs have been around for a long time, and folks making them would know how to fabricate something this small if they wanted, it is likely they know it won't be an improvement.

The practical problem with the accelerometer in your cellphone is not sensitivity these days anyway, it is drift. The industry is moving to integrate gyro and accel on one silicon substrate to give 6 axis sensing with virtually perfect mutual alignment which is important for sensor fusion (mutual correction by disambiguating the possible forces, especially keeping track of gravity). These gizmos can trivially keep up with your device orientation. What they cannot yet do is track linear movement over periods much longer than a second. So, there is this void below GPS location where it is difficult to track location accurately. Figuring out how to push the limits on drift in a portable cheap sensor is the next horizon.

I believe that this will be of great use for inertial navigation and inertial guidance. From what I remember, they tend to accumulate errors. Having a great accelerometer should help improve them. This has too many applications way beyond smartphones.

Chris, are you a real life Sheldon Cooper? This article sounds like it could have been written by that character!

I am, indeed, a socially awkward string theorist. The only difference between me and my fictional counter part is that I look better in a dress.

Ha! That's good.

I gotta say that I never knew how new user names got "classified," but I see I am a "Smack-Fu Master, in training" which I think is hysterical considering my extremely juvenile username choice! :cheers:

I think I like this forum. I'm big into cars also, but am sick of the typical car guy arguments and clashes over at The Car Lounge. Plus the intellect has been lacking over there lately. Not that there are not smart people there, but they are drowned (or is it drown, I never could figure this one out) out by the loud yelling of the others who are not so intellectual. Thing is over here I will probably be the not so smart one that is yelling! So, keep me in check!

That material choice means that the resonance frequency is just under 30kHz, allowing a researcher to potentially sense accelerations at a rate of something like 15kHz.

This statement seems to imply a connection between resonance freq. and the Nyquist freq. My signal processing-foo is pretty weak but I'm unaware of any relationship there. Anyone care to explain?

So what I think this is saying is that this system is capable of keeping up with a system where the first derivative of the acceleration has no frequency component greater than 15kHz? That makes more sense to me that stating acceleration (m/s^2) in terms on Hz (1/s).

I think it has more to do with wanting to only use the resonator at frequencies far below its resonance frequency in order to stay within a more linear part of its sensitivity regime. Apparently "something like 15kHz" (IE about 50% or less of the resonant frequency) is linear enough (which kinda makes sense, 15kHz would be the major harmonic of 30kHz, anything below that will be substantially more linear).

Not only linear, but actually almost constant (amplitude response). It's simple forced vibration on a 1 degree of freedom system.

Chris, are you a real life Sheldon Cooper? This article sounds like it could have been written by that character!

I am, indeed, a socially awkward string theorist. The only difference between me and my fictional counter part is that I look better in a dress.

Ha! That's good.

I gotta say that I never knew how new user names got "classified," but I see I am a "Smack-Fu Master, in training" which I think is hysterical considering my extremely juvenile username choice! :cheers:

I think I like this forum. I'm big into cars also, but am sick of the typical car guy arguments and clashes over at The Car Lounge. Plus the intellect has been lacking over there lately. Not that there are not smart people there, but they are drowned (or is it drown, I never could figure this one out) out by the loud yelling of the others who are not so intellectual. Thing is over here I will probably be the not so smart one that is yelling! So, keep me in check!

Ars has car guys too. You just won't find them talking about cars on the news/blog articles, you have to dig into the real forums.

the problem lies in the detection system: that laser was a relatively expensive device, and if you want your accelerometer for a few pennies, this isn't going to do it for you.

How good of a laser does this require? I would think it could use a low power diode or even laser on a chip... while they aren't pennies to my knowledge (I haven't been paying any attention to the latter in the past few years so no clue where the tech and costs are at now), I would think they're still substantially cheaper than something higher power. Pulsing shouldn't affect measurement in a system like this if you don't need the very highest frequency in your motion polling?

The problem is the bandwidth. They used a laser with a 3kHz bandwidth (a typical "expensive" narrowband laser diode has a bandwidth of around 1MHz). You need the narrow band to get large amplitude changes as the mass changes the optical length of the cavity

The problem is the bandwidth. They used a laser with a 3kHz bandwidth (a typical "expensive" narrowband laser diode has a bandwidth of around 1MHz). You need the narrow band to get large amplitude changes as the mass changes the optical length of the cavity

Thanks Chris, that makes pretty immediate sense, especially in terms of the expense I hadn't thought about that aspect.

I should note that this is unlikely to turn up in your phone anytime soon. The problem lies in the detection system: that laser was a relatively expensive device, and if you want your accelerometer for a few pennies, this isn't going to do it for you.

Whats the difference between existing phone accelerometers and this design then? Could some of its features be incorporated without a large price hike? And if they could build a cheaper accelerometer based off this design, would it work better?

The usual form of sensing involves etching a comb structure on the sides of the test mass inter-digitated with a comb on the substrate, and measuring capacitance changes. I suspect in this design the test mass is simply too small to give a good capacitor. Since the capacitor designs have been around for a long time, and folks making them would know how to fabricate something this small if they wanted, it is likely they know it won't be an improvement.

The practical problem with the accelerometer in your cellphone is not sensitivity these days anyway, it is drift. The industry is moving to integrate gyro and accel on one silicon substrate to give 6 axis sensing with virtually perfect mutual alignment which is important for sensor fusion (mutual correction by disambiguating the possible forces, especially keeping track of gravity). These gizmos can trivially keep up with your device orientation. What they cannot yet do is track linear movement over periods much longer than a second. So, there is this void below GPS location where it is difficult to track location accurately. Figuring out how to push the limits on drift in a portable cheap sensor is the next horizon.

Thanks Tanj! I understood...half of that i should just break down, cry a little, and read the actual paper. I was seeing the lazer as the load, and the drift--if I'm getting this right--is the sway of the physical component. I don't know the way cellphone accelerometers work but it does interest me.

the problem lies in the detection system: that laser was a relatively expensive device, and if you want your accelerometer for a few pennies, this isn't going to do it for you.

How good of a laser does this require? I would think it could use a low power diode or even laser on a chip... while they aren't pennies to my knowledge (I haven't been paying any attention to the latter in the past few years so no clue where the tech and costs are at now), I would think they're still substantially cheaper than something higher power. Pulsing shouldn't affect measurement in a system like this if you don't need the very highest frequency in your motion polling?

The problem is the bandwidth. They used a laser with a 3kHz bandwidth (a typical "expensive" narrowband laser diode has a bandwidth of around 1MHz). You need the narrow band to get large amplitude changes as the mass changes the optical length of the cavity

Could they make the optical cavity under the mass the actual laser cavity? Then mix the output with a constant-frequency laser on the same chip.

the problem lies in the detection system: that laser was a relatively expensive device, and if you want your accelerometer for a few pennies, this isn't going to do it for you.

How good of a laser does this require? I would think it could use a low power diode or even laser on a chip... while they aren't pennies to my knowledge (I haven't been paying any attention to the latter in the past few years so no clue where the tech and costs are at now), I would think they're still substantially cheaper than something higher power. Pulsing shouldn't affect measurement in a system like this if you don't need the very highest frequency in your motion polling?

The problem is the bandwidth. They used a laser with a 3kHz bandwidth (a typical "expensive" narrowband laser diode has a bandwidth of around 1MHz). You need the narrow band to get large amplitude changes as the mass changes the optical length of the cavity

Could they make the optical cavity under the mass the actual laser cavity? Then mix the output with a constant-frequency laser on the same chip.

I think any way you cut it you need a very high precision time basis. My guess is they'll eventually come up with something that works well enough and is cheap enough. It may not make this as cheap as current sensors, but a few cents more is probably worth it in a lot of applications....

I believe that this will be of great use for inertial navigation and inertial guidance. From what I remember, they tend to accumulate errors. Having a great accelerometer should help improve them. This has too many applications way beyond smartphones.

Vehicles tend to be big and have place high value on getting it right. So, they already have some spectacular inertial guidance systems. Even > 40 years ago they had systems capable of surviving a very rough rocket launch and warhead reentry while delivering sub 100m termination, purely on inertial guidance.

And yes, they used lasers. The descendants of these devices are on aircraft today. The gyroscopes in particular are amazing, they use interference fringes on light travelling on opposite coils of fiber optic and count the fringes' movements, which makes for astronomical (literally) accuracy and stability over hours or days. I don't happen to know how they do the accelerometer side of things.

What they cannot yet do is track linear movement over periods much longer than a second. So, there is this void below GPS location where it is difficult to track location accurately. Figuring out how to push the limits on drift in a portable cheap sensor is the next horizon.

Ah, good to know, I hadn't kept up with the state of art.

I seem to remember how they tried IR sensors to sense the reflection pattern of a room. Somewhat like the IR part of the Kinect, I imagine.

But no consumer devices for orientation surfaced. Was it too difficult?

I should note that this is unlikely to turn up in your phone anytime soon. The problem lies in the detection system: that laser was a relatively expensive device, and if you want your accelerometer for a few pennies, this isn't going to do it for you.

Chris Lee / Chris writes for Ars Technica's science section. A physicist by day and science writer by night, he specializes in quantum physics and optics. He lives and works in Eindhoven, the Netherlands.